I've read article that saturation current of the transistor is made when both junction are forward-bias, unlikely to normal operation mode that reverse-forward bias in the order from collector to emitter for NPN transistor.

The name of saturation should mean maximum current. In this "double" forward-bias, current comes from both end of the transistor and goes to...base? I think it should be since for example, after emitter current arrives base, it sees path to the collector is like barrier so should choose to go base. Same also thing happens current coming from collector.

Thus...I'm not confusion which current is saturated? Is base current saturated??

I feels this is not right conclusion but physical imaging lead me to reach this..

FWIW: Generally speaking, the "I{sat}" parameter denotes the maximum common-emitter collector current possible for a specified device operating on a specified load at a specified applied collector-circuit EMF...

Saturation of the bipolar transistor means that a further increase in the current base does not occur (almost) the increase in the collector current (emitter in reverse mode). This mode can not be called wrong. In some cases (switching circuit) or transistor in saturation or closed. Only in this mode amplifier circuit is harmful. The switching circuit base current is several times greater than the required base current for linear amplification. Sometimes datasheets indicate the saturation voltage of the transistor at a fixed base and collector currents. I advise you to study the model of Ebers-Mole.

In a circuit with an unlimited supply of collector current, adding more and more current to the base-emitter circuit will only burn the transistor. When the collector supply is limited by a resistance, the collector voltage becomes less and less until adding more base current has (almost) no effect. That is saturation of the collector circuit.

Saturation is a normal operating mode of a transistor that occurs when it is used as a switch.
As #12 noted, you apply sufficient base current so there is little reduction in collector-emitter voltage with an increase in base current.
A common value of base current to insure full saturation (turn on) of the transistor is to make the base current at least 1/10th of the collector current.